add_action( 'admin_init', 'wpdd_allow_uploads' );
function wpdd_allow_uploads() {
$contributor = get_role( 'contributor' );
$contributor->add_cap('upload_files');
}
Maggiori info https://wordpress.stackexchange.com/questions/1482/restricting-users-to-view-only-media-library-items-they-have-uploaded